6a-2(5a-4)=10a(2a+1)

Solution for 6a-2(5a-4)=10a(2a+1) equation:

6a-2(5a-4)=10a(2a+1)

We move all terms to the left:

6a-2(5a-4)-(10a(2a+1))=0

We multiply parentheses

6a-10a-(10a(2a+1))+8=0


We calculate terms in parentheses: -(10a(2a+1)), so:

10a(2a+1)

We multiply parentheses

20a^2+10a

Back to the equation:

-(20a^2+10a)


We add all the numbers together, and all the variables

-4a-(20a^2+10a)+8=0

We get rid of parentheses

-20a^2-4a-10a+8=0

We add all the numbers together, and all the variables

-20a^2-14a+8=0

a = -20; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·(-20)·8
Δ = 836
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{209}}{2*-20}=\frac{14-2\sqrt{209}}{-40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{209}}{2*-20}=\frac{14+2\sqrt{209}}{-40}
$